TCOM 501 – Networking : Theory
نویسنده
چکیده
Problem 1 [30 points]: Consider a ring network with nodes 1,2,...,K. In this network, a customer that completes service at node i exits the network with probability p, or it is routed to node i+1 with probability 1-p, for i = 1,2,...,K-1. Customers that complete service at node K, either exit the network, or are routed to node 1, with respective probabilities p and 1-p. At each node, external customers arrive according to a Poisson process with rate γ. The service times at each node are exponentially distributed with rate μ. The arrival processes and the service times at the various nodes are independent. 1. [7 points] Find the aggregate arrival rates , 1,2,..., i i K λ = . 2. [2 points] Under what conditions does the ring network have a stationary distribution? 3. [7 points] Assuming that the conditions of question 2 are satisfied, find the stationary distribution of the network. 4. [7 points] Find the average time that a customer spends in the network. 5. [7 points] Is this ring network reversible? Justify your answer.
منابع مشابه
How patients perceive the therapeutic communications skills of their general practitioners, and how that perception affects adherence: use of the TCom-skill GP scale in a specific geographical area
BACKGROUND To study: (1) the structure and test-retest reliability of a measure of how patients perceive the therapeutic communications skills of their general practitioners (TCom-skill GP), and (2) the associations of that scale with socio-demographic and health-related characteristics, and adherence. METHODS A total of 393 people who lived in the same geographic area and invited to attend a...
متن کاملResource allocation for energy efficient cellular systems
The need for more throughput in wireless cellular networks has been increasing in recent years. It has led to an increase in operational costs due to higher energy use as operators deploy more cell sites or increase transmission power at existing ones to satisfy demand. Energy costs are a major expense, and reducing them is a priority. This article presents a scheduler which aims to solve the p...
متن کامل